Solve 1/8(8/9y+8)-1/5(5/6y+1frac{2}{3})=2

$$\frac { 1 } { 8 } ( \frac { 8 } { 9 } y + 8 ) - \frac { 1 } { 5 } ( \frac { 5 } { 6 } y + 1 \frac { 2 } { 3 } ) = 2$$

Solve for y

$$y=-24$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 360, the least common multiple of 8,9,5,6,3.

$$45\left(\frac{8}{9}y+8\right)-72\left(\frac{5}{6}y+\frac{3+2}{3}\right)=720$$

Use the distributive property to multiply 45 by \frac{8}{9}y+8.

$$45\times \frac{8}{9}y+360-72\left(\frac{5}{6}y+\frac{3+2}{3}\right)=720$$

Express 45\times \frac{8}{9} as a single fraction.

$$\frac{45\times 8}{9}y+360-72\left(\frac{5}{6}y+\frac{3+2}{3}\right)=720$$

Multiply 45 and 8 to get 360.

$$\frac{360}{9}y+360-72\left(\frac{5}{6}y+\frac{3+2}{3}\right)=720$$

Divide 360 by 9 to get 40.

$$40y+360-72\left(\frac{5}{6}y+\frac{3+2}{3}\right)=720$$

Add 3 and 2 to get 5.

$$40y+360-72\left(\frac{5}{6}y+\frac{5}{3}\right)=720$$

Use the distributive property to multiply -72 by \frac{5}{6}y+\frac{5}{3}.

$$40y+360-72\times \frac{5}{6}y-72\times \frac{5}{3}=720$$

Express -72\times \frac{5}{6} as a single fraction.

$$40y+360+\frac{-72\times 5}{6}y-72\times \frac{5}{3}=720$$

Multiply -72 and 5 to get -360.

$$40y+360+\frac{-360}{6}y-72\times \frac{5}{3}=720$$

Divide -360 by 6 to get -60.

$$40y+360-60y-72\times \frac{5}{3}=720$$

Express -72\times \frac{5}{3} as a single fraction.

$$40y+360-60y+\frac{-72\times 5}{3}=720$$

Multiply -72 and 5 to get -360.

$$40y+360-60y+\frac{-360}{3}=720$$

Divide -360 by 3 to get -120.

$$40y+360-60y-120=720$$

Combine 40y and -60y to get -20y.

$$-20y+360-120=720$$

Subtract 120 from 360 to get 240.

$$-20y+240=720$$

Subtract 240 from both sides.

$$-20y=720-240$$

Subtract 240 from 720 to get 480.

$$-20y=480$$

Divide both sides by -20.

$$y=\frac{480}{-20}$$

Divide 480 by -20 to get -24.

$$y=-24$$